Definition:Finite Complement Topology/Finite
< Definition:Finite Complement Topology(Redirected from Definition:Finite Complement Topology on Finite Space)
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Definition
It is possible to define the finite complement topology on a finite set $S$, but as every subset of a finite set has a finite complement, it is clear that this is trivially equal to the discrete space.
This is why the finite complement topology is usually understood to apply to infinite sets only.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $18 \text { - } 19$. Finite Complement Topology